18. The intermittency statistics of wind power.
A specific example for the UK.

In an effort to reduce our
dependence on fossil fuel generated electricity, very large numbers of large wind turbines are
being constructed all over the world. However, the intermittent and largely unpredictable
nature of wind power has some important consequences for meeting a nation's electricity supply
needs. To illustrate this, the next two webpages contains some calculations on the intermittent nature
of wind power. The calculations on this page are specific to the UK and use actual wind speed records
at the extremities of the country. The following web page contains a generalised analysis which
can be applied to areas much larger than the UK.

It is shown that for relatively small countries like the UK, the
probability of negligible wind power contributions is so high that backup standby power sources
with essentially the same capacity as the whole mean wind power contribution will have to be
available. If the extent of the wind turbine system can be spread over larger areas like the
whole of Europe or North America, the problem is mitigated but there will still be the
probability of a few days per year when the contribution to a grid system from wind power will
fall to a very low level,

The figure on the right is based on a Meteorological Office wind map for the UK on the late
evening of 1st April 2009. This was a period when a high pressure system extended over most of
northern Europe for about a week. The wind speed figures are given in metres per second. Large
commercial wind turbines have cut-in speeds usually between 3 and 4 metres/second so that it
can be seen there would have been very few areas of the UK in which any significant wind power
would have been generated.

To quantify the matter further, data from two weather stations at Lossiemouth in Scotland and
Plymouth in the south-west of England will be considered. These two weather stations are at
opposite ends of the country and are 820 kilometres apart. They have slightly different mean
wind speeds and standard deviations so that in order to standardise later power comparisons,
the records of average daily wind speed over a three year period from 2005 to 2008 were scaled
to have the same mean wind speed of 7.5 metres per second - typical of the speed at the hub
height of a larger turbine - and the same ratio of the standard deviation to the mean speed of
52%. This is somewhat less than the 62% based on hourly wind speed data discussed in webpage 9
and is a consequence of the longer averaging period of a day compared to an hour.

The second figure shows one year's normalised wind speed data for the two weather stations. A
general reduction in wind speed in the summer months compared to the winter months can be
discerned. A measure of the relationship between the two wind speed records is the correlation
coefficient defined as

where the dashed terms u'1 and
u'2 are the fluctuating components of the wind speeds at the two weather stations and the bar
over their product means the average of their product. σ1 and σ2 are the
standard deviations of the wind speeds. If the two records were identical, the correlation
coefficient would be 1 and it would be zero if there was no relationship between them at all.
For these two records, the correlation coefficient was 0.183. This is still a significant
correlation and shows that scale of weather structures like low pressure regions are hundreds
of kilometres across. This is self-evident from the patterns of cloud cover seen in satellite
photographs of the earth and from the isobar distributions in weather maps.

The Vestas 80 metre diameter 2 megawatt turbine is used in a number of offshore wind farms
around the UK and will be used for our power calculations. The power curve for this turbine can
be seen on webpage 4. Using this power curve and the wind data for the two weather stations,
the cumulative probability distribution of the power produced by such a turbine at the two
weather stations has been calculated and is shown below. In addition, the distribution
calculated using the power output profile option in the WindPower program (webpage 3)
is also shown. From the weather station data, the mean power produced by a 'Plymouth' turbine
would be 691 kilowatts whereas the 'Lossiemouth' would produce a mean power of 726 kilowatts.
The mean power calculated using a Weibull distribution with a standard deviation of 52% of the
mean velocity was 732 kilowatts corresponding to a capacity factor 0.366. The small differences
between the results arises from the fact that the wind speed probability density distributions
for the two weather stations differ slightly from one another and also from the Weibull
distribution. Nonetheless, the distributions agree quite closely and the important point for
present purposes is to note the proportion of time that the turbines produce very low power
outputs. The results obtained from the power curve and the Weibull distribution give a
percentage time of 21% when no power at all is being produced. The results from the wind data
calculations are less than this but it is certainly the case that these turbines would produce
less than 10% of their mean power output for around 20% of the time.

We now consider the cumulative probability distribution from the mean of the power from the two
turbines. The figure below shows the distribution for this case compared with the distribution
calculated for a single turbine. The mean power will be the same as the mean power for the two
individual turbines but the standard deviation has been reduced from 99% of the mean to 76% of
the mean. It should be noted that by taking examples from opposite ends of
the UK, this cumulative probability distribution will not be significantly different from that
produced by turbines distributed over the whole UK.

The important point for the present discussion is that the period of time for which the mean
turbine power is at a low level has been reduced. The data is not sufficiently accurate to be
very precise but the period for which the power from the turbine combination drops below 10% of
the mean power is now around 10% of the time. This is a significant number of days
per year when wind power would drop to a very low level. This creates a serious problem in
planning a nation's electricity supply system. In the UK, the government target is to have 30%
of electricity supply by 2020 provided by renewable sources - which will effectively all be
provided by wind turbines. This amounts to around 15 gigawatts of electrical power.
However, for a significant number of days per year, the wind power available
would fall to less than about 1 gigawatt - equivalent roughly to one conventional power station
- and there will be the occasional periods when the power level will fall virtually to nothing.
As a result, standby sources of power will have to be available to meet this fall in capacity.
There are plans for a European grid system and, on the next webpage, the mitigating effect
of this on the period of time for which wind power falls to a very low level will be considered
by a purely analytic means. It is shown that even on a European or USA scale of wind power, the
problem remains and the cost implications of providing standby power which will remain idle for
significant periods of time will be considered. It is shown that the cost implications are less onerous
than one might intuitively expect.